Regular Article – Atomic Physics
Computational approaches to examine the vacuum polarization density
Department of Mathematics and Physics, North China Electric Power University, 071000, Baoding, China
2 Intense Laser Physics Theory Unit and Department of Physics, Illinois State University, 61790-4560, Normal, IL, USA
3 State Key Laboratory for GeoMechanics and Deep Underground Engineering, China University of Mining and Technology, 100083, Beijing, China
4 School of Physical Sciences, University of Chinese Academy of Sciences, 100190, Beijing, China
Accepted: 17 December 2022
Published online: 4 January 2023
Based on computational quantum field theory and solutions to the Dirac equation, we show how the vacuum’s polarization density induced by strong external field can be calculated based on five independent methods. We compare these methods for a spatially reduced dimensional system and show that some approaches rely on energy renormalizations, energy cutoffs or periodic boundaries. We also illustrate the spatial implications of the breakdown of the linear superposition principle for extremely high intensity fields. A main focus of the article is to discuss future challenges for each approach that might motivate new theoretical and computational studies.
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